Rebuild/ Identify

That is indeed a Rochester carburetor — installed as original equipment on 318s in '71 only; there was some kind of a strike that affected the availability of Carter carbs, so Chrysler went to Rochester to make up the volume. It does sound like time for a carb rebuild. I wouldn't doubt the fuel pump's condition just yet; at the moment it sounds like you've mostly got worn-carb issues (accelerator pump causing the hesitation, leaky needle/seat causing the extended crank time at cold start).

The best mass-market carb kits are by Walker; the best and most complete real carb kits (with jets and other repair parts not included in parts store type kits) come from The Carburetor Shop. I don't recall whether these Rochester carbs use a brass or plastic/foam float. If plastic/foam, replace. If metal, check for leaks—if none, OK to re-use.